Computational Structure of Correlative Type Higher Order Neural Units with Applications

The computational neural-network structures described in the literature are often based on the concept of linear synaptic operations. In biological processes, however, neurons form a set of very complex computing elements and perform much more complex computations than just the linear aggregation. It is well known that the computational efficiency of neural networks depends on its morphology and their learning and adaptation strategies. In our engineering design and economic processes, however, neural inputs are not necessarily the independent quantities rather they form some correlative attributes. In this paper we present a new class of correlative type higher-order neural units (HONUs) with nonlinear combinations of inputs and weights. In particular, in this paper we present a quadratic-neural unit (QNU) and a cubic-neural unit (CNU), and their higher-order extensions. For illustrating the applications of these correlative type higher-order neural units, we have given some examples taken from the field of feedback control systems and logic circuits. It has been noticed that these higher-order correlative types of neural units, both static and dynamic, can be used for many applications in various fields such as engineering, medical imaging and economics.